I think that while you are a guy here, you are also the grandpa. Family has carte blanche around newborns and share the same excitement, joy, and love as the parents.
Having a photography come in from outside this circle involves a lot of trust. There is certain a bond all mothers who have gone through child birth men simply cannot tap into. I think this is why we end up with more female newborn photographers. My wife specializes in newborn and a big portion of the job is making the moms feel comfortable and confident. What women have to go through for the nine months plus the physical and mental exhaustion after delivery is mind boggling. Having a photographer that can reassure you of your beauty and parenting capabilities moving forward sounds much better coming from someone who has also been through it. Many moms have ended up in tears just talking about it.
Does any of this mean a man can't or shouldn't do it? Not at all. But it takes a lot more than being skilled with the camera or posing.
All that being said, congratulations on the new addition to the family and for having the freedom to be there and document such an important event!